Deep excursion beyond the proton dripline. I. Argon and chlorine isotope chains

arXiv:1803.10951v5 [nucl-ex] 6 Sep 2018 Deep excursion beyond the proton dripline. I. Argon and chlorine isotope chains I. Mukha,1L.V. Grigorenko,2, 3, 4 D. Kostyleva,5, 6, ∗L. Acosta,7, 8 E. Casarejos,9A.A. Ciemny,10 W. Dominik,10 J.A. Due˜nas,11 V. Dunin,12 J. M. Espino,13 A. Estrad´e,14 F. Farinon,6A. Fomichev,2H. Geissel,6, 5 A. Gorshkov,2Z. Janas,10 G. Kami´nski,15, 2 O. Kiselev,6R. Kn¨obel,6, 5 S. Krupko,2M. Kuich,16, 10 Yu.A. Litvinov,6G. Marquinez-Dur´an,17 I. Martel,17 C. Mazzocchi,10 C. Nociforo,6A. K. Ord´uz,17 M. Pf¨utzner,10, 6 S. Pietri,6M. Pomorski,10 A. Prochazka,6S. Rymzhanova,2A.M. S´anchez-Ben´ıtez,18 C. Scheidenberger,6, 5 P. Sharov,2H. Simon,6B. Sitar,19 R. Slepnev,2M. Stanoiu,20 P. Strmen,19 I. Szarka,19 M. Takechi,6Y.K. Tanaka,6, 21 H. Weick,6M. Winkler,6J.S. Winfield,6X. Xu,22, 5, 6 and M.V. Zhukov23 (for the Super-FRS Experiment Collaboration) 1GSI Helmholtzzentrum f¨ur Schwerionenforschung GmbH, 64291 Darmstadt, Germany 2Flerov Laboratory of Nuclear Reactions, JINR, 141980 Dubna, Russia 3National Research Nuclear University “MEPhI”, 115409 Moscow, Russia 4National Research Centre “Kurchatov Institute”, Kurchatov sq. 1, 123182 Moscow, Russia 5II.Physikalisches Institut, Justus-Liebig-Universit¨at, 35392 Gießen, Germany 6GSI Helmholtzzentrum f¨ur Schwerionenforschung, 64291 Darmstadt, Germany 7INFN, Laboratori Nazionali del Sud, Via S. Sof´ıa, 95123 Catania, Italy 8Instituto de F´ısica, Universidad Nacional Aut´onoma de M´exico, M´exico, D.F. 01000, Mexico 9University of Vigo, 36310 Vigo, Spain 10Faculty of Physics, University of Warsaw, 02-093 Warszawa, Poland 11Depto. de Ingenieria Electrica y Centro de Estudios Avanzados en Fisica, Matem´aticas y Computaci´on, Universidad de Huelva, 21071 Huelva, Spain 12Veksler and Baldin Laboratory of High Energy Physics, JINR, 141980 Dubna, Russia 13Department of Atomic, Molecular and Nuclear Physics, University of Seville, 41012 Seville, Spain 14University of Edinburgh, EH1 1HT Edinburgh, United Kingdom 15Heavy Ion Laboratory, University of Warsaw, 02-093 Warszawa, Poland 16Faculty of Physics, Warsaw University of Technology, 00-662 Warszawa, Poland 17Department of Applied Physics, University of Huelva, 21071 Huelva, Spain 18Centro de Estudios Avanzados en F´ısica, Matem´aticas y Computaci´on (CEAFMC), Department of Integrated Sciences, University of Huelva, 21071 Huelva, Spain 19Faculty of Mathematics and Physics, Comenius University, 84248 Bratislava, Slovakia 20IFIN-HH, Post Office Box MG-6, Bucharest, Romania 21University of Tokyo, 113-0033 Tokyo, Japan 22School of Physics and Nuclear Energy Engineering, Beihang University, 100191 Beijing, China 23Department of Physics, Chalmers University of Technology, S-41296 G¨oteborg, Sweden (Dated: September 7, 2018. File: ar-cl-excur-f1-9.tex) The proton-unbound argon and chlorine isotopes have been studied by measuring trajectories of their decay-in-flight products by using a tracking technique with micro-strip detectors. The proton (1p) and two-proton (2p) emission processes have been detected in the measured angular correlations “heavy-fragment”+pand “heavy-fragment”+p+p, respectively. The ground states of the previously unknown isotopes 30Cl and 28Cl have been observed for the first time, providing the 1pseparation energies Spof −0.48(2) and −1.60(8) MeV, respectively. The relevant systematics of 1pand 2pseparation energies have been studied theoretically in the core+pand core+p+pcluster models. The first-time observed excited states of 31Ar allow to infer the 2p-separation energy S2p of 6(34) keV for its ground state. The first-time observed state in 29Ar with S2p=−5.50(18) MeV can be identified either as a ground or an excited state according to different systematics. I. INTRODUCTION The location of the driplines — the borderlines separating particle-stable and particle-unstable isotopes — is one of the fundamental questions of nuclear science. The unbound states with small decay energy can have lifetimes which are long enough to be treated as quasistationary states. Thus they may be considered as station- ∗[email protected] ary states in many theoretical applications. This naturally leads us to the question: what are the limits of nuclear structure existence? In other words, how far beyond the driplines the nuclear structure phenomena fade and are completely replaced by the continuum dynamics? This question represents a motivation for studies of nuclear systems far beyond the driplines. The proton and neutron driplines have been accessed for nuclides in broad ranges of Z(number of protons) and N(number of neutrons) of the nuclear chart. However, even in these regions the information about the nearest to the dripline unbound isotopes is scarce and often miss- 2 ing. Thus the fundamental question about the limits of the nuclear structure existence remains poorly investigated. For example, if we consider the proton dripline within Z≤20 (p- and sd-shell nuclei), the most extensively investigated case in that region is the fluoride isotope chain. Here our knowledge extends three mass units beyond the proton dripline: the 15F and 16F nuclides are well studied, and considerable spectroscopic information is available now for 14F [1] in addition. This paper continues our analysis of the data on reactions with a relativistic 31Ar beam populating particleunstable states [2–4]. The article [2] was focused on 30Ar and 29Cl isotopes which were reported for the first time. It was also found that the decay mechanism of 30Ar is likely to belong to a transition region between true 2p and sequential 2pdecay mechanisms. Such a “transition regime” exhibits strong sensitivity of observed kinematic variables to the values of parameters defining the decay mechanism: 2p-decay energy ET, ground state (g.s.) resonance energy in the core+psubsystem Er, and its width Γr. The practical implementations of this fact, including opportunity of a precise determination of Γrfrom the 2p correlation data, were recently elaborated in Ref. [3]. In paper [4] a detailed consideration of the data from [2] was given. In present work we report on the byproduct data of the same experiment which resulted in Refs. [2–4], which include observation of 28Cl and 30Cl ground states and several (presumably excited) states in 29Ar and 31Ar. In order to clarify the situation with the observed states, we have performed systematic studies of separation energies in the chlorine and argon isotope chains. The depth of the performed “excursion beyond the proton dripline” in the argon and chlorine isotope chains is similar now in extent to that for the fluorine isotope chain, the beststudied case in the whole Z≤20 nuclei region. II. EXPERIMENT In the experiment, described in detail in Refs. [2, 4], the 31Ar beam was obtained by the fragmentation of a primary 885 AMeV 36Ar beam at the SIS-FRS facility at GSI (Germany). The prime objective of the experiment was study of 2pdecays of 30Ar isotopes. The scheme of the measurements is shown in Fig. 1 (a). We briefly repeat the general description of the experiment and the detector performance given in Ref. [4] in detail. The FRS was operated with an ion-optical settings in a separator-spectrometer mode, when the first half of the FRS was set for separation and focusing of the radioactive beams on a secondary target in the middle of the FRS, and the second half of FRS was set for detection of heavy-ion decay products. The 620 AMeV 31Ar ions with the intensity of 50 ions s−1were transported by the first half of the FRS in order to bombard a 9Be secondary target located at the middle focal plane S2. At the first focal plane S1 of the FRS, an aluminum wedge degrader was (b) S1 S4 S0 S1 secondary beam tracking hi-resolution tracking of HI 36 Ar transversal reconstruction plane degrader wedge primary target secondary target OTPC studies of stopped ions FRS micro-strip detectors reconstructed reaction vertex secondary beam p 2 (HI- p 2 ) (HI- p 1 ) p 1 HI: 27 S or 29 S 31 Ar thick Be target S1 S2 S3 area (a) FIG. 1. Sketch of the experiment at the FRS fragment separator. (a) General layout, see details in [4]. Primary 36Ar beam hits a target at S0, and a secondary beam of 31Ar is selected and focused on the middle focal plane S2 by using a wedge degrader at S1. Nuclei of interest 31Ar∗,29Ar are produced in the secondary target at S2 in in-elastic scattering and two-neutron knock-out reactions. Heavy-ion decay products 29,27S are identified by their energy-loss and time-of-flight as well as the magnetic rigidity by using the standard beam detectors at S2 and S4. At S4, the studies of stopped ions can be performed by using Optical Time Projection Chamber OTPC. (b) The detector setup downstream of the secondary target at S2, where the trajectories of an incoming 31Ar ions, the decay products 27,29S and the protons (i.e., p1, p2) are measured. installed in order to achieve an achromatic focusing of 31Ar at the secondary target. In the previously reported data [4] the 30Ar nuclei were produced via one-neutron (−1n) knockout from the 31Ar ions. The decay products of unbound 30Ar were tracked by a double-sided silicon micro-strip detector array placed just downstream of the secondary target, see Fig. 1 (b). The projectile-like particles, outgoing from the secondary target, were analyzed by the second half of the FRS, which was operated as a magnetic spectrometer. The magnet settings between the S2 and S4 focal planes were tuned for the transmission of the targeted heavy ion (HI) fragments (e.g., 28S) down to S4, the last focal plane. In addition to 30Ar, the studies of decay properties of the stopped 31Ar ions were performed by using the OTPC detector at S4 [5]. A double-sided silicon micro-strip detector (DSSD) array consisted out of four large-area DSSDs [6] was employed to measure hit coordinates of the two protons and the recoil heavy ions, resulting from the in-flight decays of the studied 2pprecursors. The high-precision position measurement by DSSDs allowed for reconstruction of all fragment trajectories, which let us to derive the decay vertex together with an angular HI-pand HI-p-p correlations. For example, the trajectories of measured 28S+p+pcoincidences were a basis for the analysis and the concluded spectroscopic information on 30Ar [4]. 3 (iv) (iii) (ii) (i) p 2- 29 S (mrad) p1 - 29 S (mrad) FIG. 2. Angular correlations θp1-29 S−θp2-29 S(in mradians) produced from the measured 29S+p+pcoincidence indicating 2pdecays of 31Ar excited states. The shaded arcs labeled by the Roman numerals point to four selected areas where the 2p-decay events have the same decay energy. The data symmetry respective proton permutations is illustrated by the 45◦-tilted diagonal dash-dot line. However, a number of by-product results were obtained in a similar way from the data recorded in the same experiment. Namely, excited states of 31Ar were populated by various inelastic mechanisms, and 29Ar spectrum was populated in two-neutron (−2n) knockout reaction. The unbound 31Ar and 29Ar states were detected in triple 29S+p+pand 27S+p+pcoincidences, respectively, see the respective angular correlation plots in Figs. 2 and 3. The relative angles there and everywhere below are presented in milliradian units (mrad). Also the states of 28Cl and 30Cl can be populated both in the fragmentation of 31Ar and as the result of proton emission from the corresponding 31,29Ar isotopes. These mechanisms have lower cross sections, and the obtained results have less statistics, see the respective angular p-HI correlation plots in Figs. 9 and 6. In spite of poor statistics with few events registered, we have obtained several nuclear-structure conclusions from the experimental data. A. How nuclear-structure information can be obtained from proton-ion angular correlations Before the data analysis presentation, we remind the reader, how nuclear-structure information concerning the nuclei involved in a 1por 2pdecay can be obtained by measuring only the trajectories of the decay products, without measuring their kinetic energies. This approach has been successfully tested in analyses of 1p, 2pdecays of the known states in 19Na, 16Ne and has been described in details in Ref. [7]. 20 30 40 50 60 70 80 90 100 110 20 30 40 50 60 70 80 90 100 110 p 2 - 27 S (mra d) p 1 - 27 S (mrad) FIG. 3. Angular correlations θp1-27 S−θp2-27 S(in mradians) produced from the measured 27S+p+pcoincidence. The shaded arc where the 2p-decay events have the same decay energy indicates on a 29Ar state. FIG. 4. Sketches of decay schemes expected for three simple mechanisms of 2pdecay from a 2p-precursor with mass number Ato a daughter nucleus with A−2 (illustrated in the upper panels). The respective cartoons of transverse momentum correlations kp1-HI −kp2-HI are shown in the lower panels: (a) prompt or direct 2pemission (three-body decay); (b) sequential emission of protons via a narrow intermediate state in nucleus A−1; (c) de-excitation of broad continuum states in the nucleus Ato a single low-lying resonance in the intermediate nucleus with A−1. For the discussion of 2pdecays given below, let us consider three different mechanisms. These cases are illustrated in Fig. 4. The upper panels schematically show the nuclear states involved in 2pdecay of nucleus with mass number A, the lower panels show the corresponding momentum correlations kp1-HI −kp2-HI, where HI corresponds to the A−2 nucleus. In the first case (a) of prompt 2pdecay, sequential 2pemission should be energetically forbidden. As both emitted protons should share 2p- 4 d p-HI p-HI p-HI (max) ~ k p-HI dW / d p-H I p-HI k p2 -HI (c) (b) (a) k 3R k p1-HI k 2R k 2R FIG. 5. (a) Cartoons of transverse momentum correlations kp1-HI −kp2-HI for a case of two precursor states with prompt and sequential 2p-decay mechanisms. (b) Kinematics of isotropic mono-energetic proton emission from a high-energy heavy ion HI. (c) The corresponding angular p-HI distribution exhibiting the peak, corresponding to the Q-value of the 1pdecay. decay energy Q2p, their energy spectra are broad and centered around the value of Q2p/2; consequently, the 2p momentum-correlation plot should have the shape of an arc, with a radius corresponding to the Q2pvalue and with most of the counts lying in the peak indicated by the dark spot in the lower panel of Fig. 4 (a). Note that all momentum-correlation plots in Fig. 4 are symmetric with the respect to the 45◦line since the protons p1and p2are indistinguishable. The case (b) represents the sequential emission of two protons through a narrow resonance in the intermediate nucleus with A−1. The proton energies are fixed here, and the kp1-HI−kp2-HI correlation plot should yield double peaks as indicated by the black dots in the lower panel of Fig. 4 (b). The third 2p-decay mechanism is 2pemission from several broad continuum parent states via a low-lying state in A−1, see Fig. 4 (c). This mechanism should reveal a peak in the p-HI energy with the corresponding broad distribution along the narrow “slice” as shown in the lower part of Fig. 4 (c). In the present method, we measure only total HI momentum and relative p-HI angles in the transverse direction. We register trajectories of all decay products directly downstream from the secondary-reaction target. Fig. 5 (b) shows the kinematics plot for the simple case of isotropic and mono-energetic single-proton emission from a high-energy heavy ion. Fig. 5 (c) shows the corresponding distribution of laboratory p-HI opening angles, θp-HI. The angular spectrum exhibits a sharp peak corresponding to the proton emitted almost orthogonal to the HI momentum vector. Thus the maximum value of θp-HI is directly related to the decay energy Qpof the emitted proton. In the same way, the kp1-HI −kp2-HI momentum correlations for 2pdecays (Fig. 5) can be replaced by the corresponding θp1-HI −θp2-HI correlations. If the initial and final states of pemission are narrow, the width of a peak in the angular distribution is governed mostly by the angular straggling of the proton in the secondary-reaction target. If those states are broad, the width results from a convolution of the state’s width with the proton angular straggling. The cases, sketched in Figs. 4 and 5 represent ideal cases. In reality, several proton branches may be present, representing more than one of the cases, shown schematically in Fig. 5 (a), and leading to a complicated spectra with several peaks. One can, however, clean up the spectra and enhance e.g. transitions with the small Q2p-values by gating on the small angles of θp1-HI and plotting the spectrum of θp2-HI under this condition. Another tool of data analysis is a kinematic variable ρθ=qθ2 p1-HI +θ2 p2-HI , describing 3-body HI+p+pangular correlations. Since ρθ is related to the energy sum of both emitted protons and, therefore, to the Q2pof the parent state by the relation Q2p∼ρ2 θ[8], one can obtain an indication of the parent state and its 2p-decay energy by studying the distribution of ρθ. In a case of the decay from the same state, two protons share Q2p, and such events should be located along a root-mean-square arc in an angular correlation plot θp1-HI −θp2-HI. By gating on a particular ρθarc, the decay events from a certain 2p-precursor can be selected. The ρθdistributions are very useful in the analysis of 2p-decay data since they produce the spectra with less peaks and allow to gate on a specific excitation-energy regions. In all cases, detailed Monte-Carlo simulations are required in order to interpret the angular spectra quantitatively by taking into account the corresponding response of the experimental setup. For example, the angular correlation for fixed energy decay must be first calculated. This predicted angular correlation is then compared to the measured one. The resonance energy is obtained by the best-fit where the probability that the two distributions are identical has maximum value. In the same way, limits for the width of a resonance can be obtained. The above-described analysis procedure, where the states observed in a 2p-precursor were investigated by comparing the measured angular θand ρθcorrelations 5 30 40 50 60 70 80 90 100 60 70 80 90 100 110 0 2 4 6 8 events Q p (MeV) (a) (b) ( 27 S+ p + p ) ( mrad) (mrad) 29 Ar FIG. 6. The angular correlation plot θ−ρθ(angles are in mradians) for 29Ar decay via 27S+p+pchannel is shown in (b). The hatched area highlights events from the decay of a27S+presonance assigned as the 28Cl ground state. The dotted lines guide the eye for the regions corresponding to assumed 29Ar states. (a) shows the angular correlations θp-27S (shaded histogram) obtained as projection on the θaxis from the 27S+p+pchannel of (b). The θp-27 S“inclusive” angular correlations obtained from the measured p-27S coincident events are shown by the black hollow histogram. The labeled (1)–(4) arrows highlight the events inspected for the possible 28Cl resonance states. The upper axis shows the corresponding 1p-decay energies Qp. The 45◦-tilted dotted line in (b) shows the kinematical limit. with the Monte Carlo (MC) simulations of the respective detector response, has been published in Refs. [7, 8]. We follow this procedure in the present work, and the applied detector calibrations are taken from the previous 30Ar analysis of the same experiment [4]. B. The data analysis: unknown states in 29Ar and 28Cl We begin from the analysis of the relatively simple case of the measured 27S+p+pcorrelations presented by the θp1-27S−θp2-27 Sand θ−ρθplots in Figs. 3 and 6(b), respectively. These 29Ar-related correlations com- 1.4 1.5 1.6 1.7 0.0 0.5 1.0 25 30 35 40 45 50 0 1 2 3 4 Intensity (counts) ( 27 S-p) (mrad) Probability Decay energy (MeV) FIG. 7. Best fit of the peak (1) of the θp-27 S“inclusive” angular correlations from Fig. 6(b) (histogram) by simulations of the setup response to in-flight decays of 28Cl with the 1p- decay energy of 1.60 MeV (dashed curve). The inset shows probability that the simulated distribution matches the data as function of the 1p-decay energy. prise just seven 2p-decay events, each being measured in triple 27S+p+p coincidence. Each detected event provides two θp-27Sand one ρθvalues. Most of them are very well focused around the locations at θ= 44 mrad or ρθ= 84 mrad. These values correspond to the 1p-decay of the 28Cl state with Erof about 1.6 MeV and to the 2p-decay of the 29Ar state with Q2pof about 5.5 MeV. A cross-check of this conclusion is illustrated in Fig. 6(a) where the angular correlations θp-27 Sprojected from the 27S+p+pcorrelation plot [in Fig. 6(b)] are compared with the “inclusive” θp-27 Sdistribution obtained from the measured p-27S double-coincidence events. One may see that the “inclusive” spectrum consists of relatively enhanced peaks (1–3). The peaks (1) and (2) have the best-fits at the 1p-decay energies Erof 1.60(8) and 3.9(1) MeV, respectively. They have been assigned as the first- and second-emitted protons from the 5.5 MeV state in 29Ar, and their sum decay energy gives the total 2p-decay energy of 5.50(18) MeV. The data-fitting procedure is illustrated on the example of the (1) peak at θ= 44 mrad in the p-27S correlation in Fig. 7. This is the same procedure described in details in Refs. [4, 7]. The best-fit simulations obtained for the in-flight decay of 28Cl with the 1p-decay energy of 1.60 MeV describe the data quantitatively, and the figure inset shows that the probability of the data matching simulations is about 1. The full width at half maximum of the probability distribution provides the evaluation of the Eruncertainty. There are two additional events in the decay patten of the 5.5 MeV state in Fig. 6 (b) corresponding to the inclusive peaks (3) and (4) in Fig. 6 (a). As the inclusive peak (3) is much enhanced, we may speculate that it may be an evidence on the second state in 28Cl, which is also fed by the other unspecified reaction channels, illustrated in Fig. 4(c). The best-fit 1p-decay energy of the peak (3) 6 0 1 2 3 4 5 6 7 8 9 1 p 1 p 3.20(6) 0.0, 5/2 + 1.60 (8) [9.5] [7.2 ] 5.50(18) [2.1-2.9] ? 27 S+2 p 29 Ar 28 Cl+ p E (MeV) FIG. 8. The suggested decay scheme and the energy levels of 29Ar and 28Cl relative to the 27S+2pthreshold. The grayshaded region corresponds to the ground state energy of 29Ar predicted in this work, see the discussion in section IV. The assumed and indicated 1ptransitions are shown by the solid and dotted arrows, respectively. The dotted levels indicate very tentative assignments made on the basis of one or two 2p-decay events. is 3.20(6) MeV. In addition, there are indications on 27S+p+pcorrelations at ρθof 97 and 112 mrad, which may correspond to the 2p-decays of 29Ar with Q2pof about 7.2 and 9.5 MeV, respectively. Both of the indicated states have the second-emitted proton energy of 1.6 MeV, which corresponds to the lowest assigned state in 28Cl. The derived decay scheme and levels of 29Ar and 28Cl are shown in Fig. 8. We argue below in Section III, that our empirical assignments are backed by the isobaric mirror symmetry systematics and that the most probable interpretation of the measured decay-product correlations is the observation of 28Cl ground state with Sp= -1.60(8) MeV and the 29Ar excited state with S2p= -5.50(18) MeV. C. The data analysis: unknown states in 31Ar and 30Cl The 2p-decay pattern of 31Ar, derived from the 29S+p+pdata, is more complicated. Several separated regions with events, corresponding to the same 2p-decay energy, can be distinguished at the low angles in Fig. 2, which indicate different states in 31Ar. The tentatively selected arcs are labeled by the Roman numerals (i)–(iv). The same event groups can be found in the angular θ−ρθ correlation plot in Fig. 9 (c) derived for the assumed 31Ar 10 20 30 40 50 60 70 30 40 50 60 70 80 90 100 110 0 5 10 events 30 40 50 60 70 80 0 5 10 15 20 Q 2 p (MeV) 54 3 2 (v) (iii) (iv) (ii)(i) (b) events ( 29 S+ p + p ) (mrad) (a) 1 (c) n = 1 n = 2 n = 3 n = 4 ( 29 S+ p + p ) (mrad) (mrad) 31 Ar FIG. 9. The angular correlation plot θ-ρθderived for the measured 29S+p+pchannel (c). The (a) and (b) show corresponding projections on the ρθand θaxes, respectively. The hatched areas in (c) highlight events assumed to originate from the decay of 30Cl resonance states. The dotted lines in the (a) and (c) guide the eye for the regions corresponding to the assumed 31Ar states which correspond to the events highlighted by the arcs in Fig. 2 labeled by the Roman numerals. The arrows and vertical lines in (a) point to the regions inspected for possible states in 31Ar. The cases (i)- (v) correspond to the events highlighted by the arcs (i)-(v) in Fig. 2, respectively. The upper axis shows the 2pdecay energy Q2pin the 29S+p+psystem. The inclined dotted line in (c) shows the kinematic limit for this type of plot; shape coding corresponds to multiplicity of events. 2p-decays. Its projections on the θand ρθaxes are shown in the panels (b) and (a) in Fig. 9, respectively. The θ(29S-p) projection indicates some structures centered at the angles θ={26,37,43}mrad, which point to possible low-energy states in 30Cl. The ρθprojection indicates several 2p-decay patterns in 31Ar with the centre- of-gravity values at ρθ={45,53,61}mrad. The obtained statistics of the measured triple coincidences is low, and the non-selective projections do not 7 allow for a quantitative analysis. Thus we have used the slice θprojections gated by the ρθselected areas (iv) in Fig. 9 (a). These gated projections are shown in Fig. 10 in the panels (i-v), respectively. Two additional projections gated at very large ρvalues are shown in the panels (vi,vii). In analogy to the 29Ar analysis, the “inclusive” θp-29 Sdistribution obtained from the measured p-29S double-coincidence events is shown in the lowest panel of Fig. 10. This inclusive distribution display the same low-energy peak (1) at around 26 mrad as well as the peaks (4,5), though evidence on the Fig. 9(c)- indicated peaks at 37 and 43 mrad (marked as (2) and (3), respectively) is weak. Similarly to the 28Cl case, the MC simulations of the well-distinguished peaks (1,4,5) in the lowest panel of Fig. 10 by the experimental-setup response have resulted in assigning of the unknown 30Cl states with the 1p-decay energies Erof 0.48(2), 2.00(5) and 3.0(2) MeV, respectively. On the basis of the performed analysis, the 0.48(2) MeV peak is assumed to be the ground state of 30Cl. Such an assignment is supported by the observed 29S+p+pcorrelations where one of the emitted protons has relatively large energy and another proton’s energy is peaked at around 0.5 MeV, see Fig. 10(vii). This is a typical situation for a final-state interaction due to the 30Cl g.s. resonance, see illustration in Fig. 4(c). By using the parameters of the 30Cl g.s. one may obtain the 2p-decay energy of the lowest-energy state in 31Ar observed in the 29S+p+pcorrelations, see Fig. 10(i). We have fitted the θprojection (i) by a sequential proton decay of 31Ar via the g.s. of 30Cl, and the obtained value of 2p-decay energy is 0.95(5) MeV. Though the pattern centered at ρθ= 35 mrad has low statistics, it is very important for an overall interpretation of the data, as it highly likely corresponds to the 31Ar first excited state. Thus we may lay the first piece into the puzzle of the 31Ar excitation spectrum and its 2p-decay scheme whose complete reconstruction is shown in Fig. 11 and which is explained in a step-by-step way below. •Namely, the gated θprojections in Fig. 10 (ii) and (iii) exhibit the same peak (3) at 43 mrad, which point to the sequential 2pdecays of these 31Ar states via the same state in 30Cl. The peak (3) is best-fitted by assuming the 1pdecay of the 30Cl state with Er=1.35(5) MeV. Then the 31Ar states corresponding to the complementary bumps in the structures (ii) and (iii) have the fitted 2p-decay energies of 1.58(6) and 2.12(7) MeV, respectively. One should note that the projection (ii) provides very broad and statistically poor signal from the corresponding 31Ar state, which makes the assignment very tentative, see Fig. 11. •Next, the gated θprojections in Fig. 10 (iv) and (v) reveal events matching the same 2.00 MeV peak (4) in the inclusive spectrum in the lowest panel in Fig. 10. They point to the sequential 2pdecays of two more states in 31Ar via the 2.00 MeV state in 0 2 4 68< <72 (v) 58< <63 (iv) 52< <55 (iii) 44< <49 (ii) 34< <37 (i) 2.0 3.0 3.5 2.5 1.5 1.0 (5) (4) (3) (2) 0.5 E ( 29 S- p ) (MeV) (1) 0 2 4 0 2 4 ( 29 S- p ) (mrad) Intensity (counts) 0 3 6 0 3 6 0 2 4 95< <120 (vii) 75< <81 (vi) 10 20 30 40 50 60 70 0 3 6 10 20 30 40 50 60 70 0 5 10 15 2. 3.0 3.5 2.5 1.5 1.0 (5) (4) (3) (2) 0.5 E ( 29 S- p ) (MeV) (1) Intensity (counts) ( 29 S- p ) (mrad) FIG. 10. The “gated” angular correlations θp-29 Sderived from the measured 29S+p+ptriple-coincidence events, which are selected by choosing the gate conditions within the ρθ ranges corresponding to the highlighted arcs in Fig. 2. The panels (i)–(iv) correspond to the selection gates labeled in Fig. 2 by the same Roman numerals. The additional panels (v)–(vii) present the similar θp-29Scorrelations selected by the larger ρθvalues shown in their upper-left corners. The panel (viii) shows the “inclusive” angular θp-29 Scorrelations obtained from the measured 29S+pdouble coincident events (the hollow histogram). The upper axes show the corresponding energies in the 29S+psystem. The arrows (1)–(5) point to the events inspected for possible resonances in 30Cl as well as the vertical across-panel lines. 30Cl. In particular, the fit of the peak at ∼48 mrad which is complementary to the peak (4) in the pro- 8 jection (v) yields its energy of 1.56(10) MeV, and together they allow for assignment of the new 31Ar state with the 2p-decay energy of 3.56(15) MeV, see Fig. 11. Interpretation of the θprojections in Fig. 10 (iv) is more complicated, because it has the additional components, and one of them matches the peak (2) at 37 mrad due to a suspected state in 30Cl. •The contribution of such a state can be spotted also in the θprojection (vi) in Fig. 10 as well as in the “inclusive” θdistribution labeled as (2). The corresponding fits provide the 1p- decay energy of 0.97(3) MeV assigned to the 30Cl state. Then the whole structure of the θdistribution (iv) in Fig. 10 may be explained by a sequential 2p-decay of one state in 31Ar by two branches via the intermediate 0.97 and 2.00 states in 30Cl. The respective fits provide two independent evaluations of the 2p-decay energy of the 31Ar state of 0.97(3)+1.65(10)=2.62(13) and 2.00(5)+0.45(3)=2.45(8) MeV, respectively. They agree within the statistical uncertainties. One may note that the assigned 2p-decay branch via the 2.00 MeV state in 30Cl has the first-emitted proton energy of 0.45(3) MeV, which coincides with the 1p-decay energy of the g.s. of 30Cl. Therefore the sequential 2pdecay may proceed also via the g.s. of 30Cl. These two assignments indistinguishable in our experiment are shown in Fig. 11 by the dotted arrows. Due to this uncertainty, we accept the 31Ar state to be at 2.62(13) MeV. •Finally, the gated θprojection in Fig. 10 (vi) with the assumed peak (2) due to the 0.97 MeV state in 30Cl allows for identification of the highest state observed in 31Ar with the 2p-decay energy of 0.97(3)+3.2(2)=4.2(2) MeV. •The only undiscussed peak (5) at about 65 mrad in the “inclusive” θdistribution in the lowest panel of Fig. 10 is also detected in the observed 29S-p-p correlations, see Fig. 9(b). However, energy of another emitted proton is distributed in a broad range of energy, which points to a continuum region of 31Ar excitations above 5 MeV. Therefore the peak (5) can not be assigned to an individual 31Ar state. We may speculate that it probably belongs to the 3.0(2) MeV state in 30Cl which is strongly populated by de-excitation of high-energy continuum in 31Ar. Summarizing the above considerations, we have assigned the 30Cl states with the decay energies Erof 0.48(2), 0.97(3), 1.35(5), 2.00(5) and 3.0(2) MeV. There is also some indication that the structure around θ= 26 mrad may consist of two sub-structures at about 24 and 28 mrad (corresponding to the Ervalues of 0.48 and 0.55 MeV, respectively), which we will discuss below. The newly prescribed states in 31Ar have the 2p-decay 0 1 2 3 4 10.217 10.803 11.280 1/2 (+) ,3/2 (+) 11.946 (1/2,3/2) 12.893 5/2 + 31 Al 1.22 1/2 + 4.2(2) 2.62(13) 2.12(7) 1.58(6) 3.0(2) 2.00(5) 1.35(5) 1 p 1 p 0.0 5/2 + 0.97(3) 0.48(2) 0.006(34) 0.95(5) 29 S+2 p 31 Ar 30 Cl+ p E (MeV) 3.56(15) FIG. 11. The decay and level schemes for 31Ar and 30Cl isotopes derived from the data. The assigned 1ptransitions are shown by the light gray solid arrows. The dotted arrows show two undistinguished decay branches of the 2.62(13) state in 31Ar, and the dashed arrow indicates 1ptransitions from unidentified states in 31Ar feeding the 3.0(2) state in 30Cl. Vertical axis shows the energies relative to proton (for 30Cl) and two-proton (for 31Ar) breakup thresholds. The four lowest excited states of isobaric mirror partner 31Al are aligned with corresponding observed states of 31Ar (the correspondence of the levels is shown by red dashed arrows) and the 31Ar g.s. energy is inferred based on isobaric symmetry assumptions. The legends for 31Al levels show energies relative to the 2p-breakup threshold and spin-parity Jπof the state. energies of 0.95(5), 1.58(6), 2.12(7), 2.62(13), 3.56(15) and 4.2(2) MeV. All derived levels in 31Ar and 30Cl and their decay transitions are shown in Fig. 11. III. SYSTEMATICS FOR CHLORINE ISOTOPES As a first step in the interpretation of the data, we would like to evaluate the energies of the states in protonrich chlorine isotopes systematically by using the known information about their isobaric mirror partners. The obstacle here is the Thomas-Ehrman shift (TES) effect [9, 10], especially pronounced in the s-dshell nuclei. The systematics of orbital size variations for s- and d-wave configurations are different when approaching the proton dripline and beyond it. This leads to a significant relative shift of the s-wave and d-wave dominated states distorting the expected (due to isobaric symmetry) nuclear level ordering in isotopes near the proton dripline. The core+pcluster model is a reasonable tool for consideration of this effect. The Coulomb displacement energies in the core+pcluster model depend on two parameters: the orbital radius, which is mainly controlled by the potential radius, and the charge radius of the core. We use the potential with a Woods-Saxon formfactor and with a conventional dif- 9 28 30 32 34 36 38 40 42 3.2 3.3 3.4 3.5 3.6 3.7 24 26 28 30 32 34 36 3.1 3.2 3.3 3.4 3.5 Ar, exp. r ch (Ar) (fm) Mass number Ar S, exp. S, lower S, upper r ch (S) (fm) Mass number S expected dripline FIG. 12. Charge radii of sulphur isotopes used in the cluster core+pmodel for chlorine states. The dependence for sulphur isotopes is aligned with the much better studied dependence for argon isotopes to substantiate the provided extrapolation. fuseness parameter a= 0.65 fm. The radius value is provided by the standard parameterizations r0= 1.2(Acore + 1)1/3.(1) The charge radii of sulphur isotopes are poorly studied [11], so we use the extrapolation shown in Fig. 12. Here we use two limits, corresponding to either ascending or descending trend near the dripline (both trends are not excluded by the available systematics of the charge radii). One should note that the 26S case is already uncertain. This particle-unstable nuclide (expected to be a 2p-precursor [12]) has the valence-proton wave function expected to well penetrate into the sub-barrier region. Then the Coulomb potential of the charged sphere is used with the radius parameter rsph, r2 sph = (5/3)[r2 ch(Acore) + r2 ch(p)] ,(2) where rch(p) = 0.8 fm. The potential parameters are collected in Table I. The results of the calculations are collected in Fig. 13. Below, we study the chain of five chlorine isotopes 32−28Cl. A. 31Cl and 32Cl cases One can see in Fig. 13 (a,b), that for known isotopes 31Cl and 32Cl the used systematics of potential parameters given by Eqs. (1) and (2) provides level energies which are overbound a bit (by ∼150 keV) in comparison with the data. However, the general trend is well reproduced, thus the standard set of the parameters could be the good starting point for the systematic evaluation of the whole isotope chain. B. 30Cl and 29Cl cases Spectrum of 29Cl was discussed in details in [2, 4], see Fig. 13 (d). The data on 30Cl spectrum is reported in this work for the first time. The spectra of these isotopes can be reasonably interpreted only on the bases of the strong TES effect for some states. The calculated levels shown in Fig. 13 (c) present evidence that two low-lying structures in the spectrum of 30Cl (at 0.48(2) and 0.97(3) MeV) can be associated with nearly-overlapping doublets 2+–3+and 1+–3+. We assume that the 3+g.s. in 30Al has a d-wave structure. Then its doublet partner, the 2+ state is expected to be strongly shifted down by TES, and therefore to become the 30Cl g.s. There is a hint in the data shown in Figs. 9 and 10, that the “ground state peak” in 30Cl at θ= 26 mrad actually consists of two substructures, differently populated in the decays of several 31Ar states. In this work, the 30Cl g.s. prescription is based on the lower substructure with the corresponding proton emission energy Er= 0.48 MeV. Why the above-mentioned prescription is reliable? The Thomas-Ehrman shift for the 30Al-30Cl g.s. pair is about 330 keV. If we assume that the 3+g.s. in 30Al has an swave structure, then the Thomas-Ehrman shift leads to the evaluated energies Er= 50 −150 keV of the 3+g.s. in 30Cl. For such low decay energies, the 30Cl g.s. should live sufficiently long time in order to “survive” the flight through the second achromatic stage of the FRS fragment separator (of ∼150 ns). We don’t report such an experimental observation. We may also assume a d-wave structure of the 2+and second 3+states. However such an assumption practically does not change the predicted Spenergy of 30Cl, but it requires the existence of peaks which are not seen in our data. C. 28Cl case A doublet of low-lying states can be found in the bottom of 28Na spectrum, see Fig. 13 (e). Presumably, the 2+and 1+states are separated by just of ∼50 keV. The 1+state can be only d-wave dominated, while 2+can be either s-wave or d-wave dominated. If both states have TABLE I. Potential parameters for the cluster two-body ACl=A−1S+pmodel. The minimum and maximum rsph values correspond to the charge radii estimated from Fig. 12. A r0rsph(min) rsph(max) Vs(MeV) Vd(MeV) 32 3.81 4.31 4.32 −46.80 31 3.77 4.29 4.31 −45.00 −45.38 30 3.73 4.26 4.31 −45.10 −44.76 29 3.69 4.23 4.33 −41.87 −41.85 28 3.64 4.20 4.38 −42.52 −42.69 27 3.60 4.16 4.45 −34.85 −39.51 26 3.56 4.12 4.55 −32.80 −38.86